As we know an axillary bud differentiates to form a floral bud, but what is a floral primodium?
A primordium (plural: primordia) is the first recognizable manifestation of a biological structure. In the case of a flower this will be a small meristematic bump typically at the periphery of a shoot apical meristem.
In contrast, a flower bud is generally used to describe the entire structure including the meristem and any associated structures (such as bracts) that can develop into a flower. This structure often goes through a period of dormancy.
Another way of saying this is that, in the context of a flower, a primordium is a group of meristematic cells that has not yet formed any lateral structures, while a bud contains a meristem and its associated lateral structures. Note however, that I believe I've seen bud used as a synonym for primodium in some cases.
Another difference is that primordia are (usually) microscopic structures, while buds are (usually) macroscopic (visible to the unaided eye) structures.